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Computer programs and models are playing an increasing role in simulating vehicle crashworthiness, dynamic, and fuel efficiency. To maximize the effectiveness of these models, the validity and predictive capabilities of these models need to be assessed quantitatively. For a successful implementation of Computer Aided Engineering (CAE) models as an integrated part of the current vehicle development process, it is necessary to develop objective validation metric that has the desirable metric properties to quantify the discrepancy between multiple tests and simulation results. However, most of the outputs of dynamic systems are multiple functional responses, such as time history series. This calls for the development of an objective metric that can evaluate the differences of the multiple time histories as well as the key features under uncertainty.

A copula-based approach for model bias characterization was previously proposed [18] aiming at improving prediction accuracy compared to other model characterization approaches such as regression and Gaussian Process. This paper proposes an adaptive copula-based approach for model bias identification to enhance the available methodology. The main idea is to use cluster analysis to preprocess data, then apply the copula-based approach using information from each cluster. The final prediction accumulates predictions obtained from each cluster. Two case studies will be used to demonstrate the superiority of the adaptive copula-based approach over its predecessor.

To date, model validation metric is prominently designed for non-dynamic model responses. Though metrics for dynamic responses are also available, they are specifically designed for the vehicle impact application and uncertainties are not considered in the metric. This paper proposes the validation metric for general dynamic system responses under uncertainty. The metric makes use of the popular U-pooling approach and extends it for dynamic responses. Furthermore, shape deviation metric was proposed to be included in the validation metric with the capability of considering multiple dynamic test data. One vehicle impact model is presented to demonstrate the proposed validation metric.

Simulation based design optimization has become the common practice in automotive product development. Increasing computer models are developed to simulate various dynamic systems. Before applying these models for product development, model validation needs to be conducted to assess their validity. In model validation, for the purpose of obtaining results successfully, it is vital to select or develop appropriate metrics for specific applications. For dynamic systems, one of the key obstacles of model validation is that most of the responses are functional, such as time history curves. This calls for the development of a metric that can evaluate the differences in terms of phase shift, magnitude and shape, which requires information from both time and frequency domain. And by representing time histories in frequency domain, more intuitive information can be obtained, such as magnitude-frequency and phase-frequency characteristics.

Design optimization methods are commonly used for weight reduction subjecting to multiple constraints in automotive industry. One of the major challenges remained is to deal with a large number of design variables for large-scale design optimization problems effectively. In this paper, a new approach based on fuzzy rough set is proposed to address this issue. The concept of rough set theory is to deal with redundant information and seek for a reduced design variable set. The proposed method first exploits fuzzy rough set to screen out the insignificant or redundant design variables with regard to the output functions, then uses the reduced design variable set for design optimization. A vehicle body structure is used to demonstrate the effectiveness of the proposed method and compare with a traditional weighted sensitivity based main effect approach.

One of the major challenges in multiobjective, multidisciplinary design optimization (MDO) is the long computational time required in evaluating the new designs' performances. To shorten the cycle time of product design, a data mining-based strategy is developed to improve the efficiency of heuristic optimization algorithms. Based on the historical information of the optimization process, clustering and classification techniques are employed to identify and eliminate the low quality and repetitive designs before operating the time-consuming design evaluations. The proposed method improves design performances within the same computation budget. Two case studies, one mathematical benchmark problem and one vehicle side impact design problem, are conducted as demonstration.

Particle swarm optimization (PSO) is a relatively new stochastic optimization algorithm and has gained much attention in recent years because of its fast convergence speed and strong optimization ability. However, PSO suffers from premature convergence problem for quick losing of diversity. That is to say, if no particle discovers a new superiority position than its previous best location, PSO algorithm will fall into stagnation and output local optimum result. In order to improve the diversity of basic PSO, design of experiment technique is used to initialize the particle swarm in consideration of its space-filling property which guarantees covering the design space comprehensively. And the optimization procedure of PSO is divided into two stages, optimization stage and improving stage. In the optimization stage, the basic PSO initialized by Optimal Latin hypercube technique is conducted.